Hello! How question regarding export to MTX.
When I do publisher->SaveMTXFile() it saves information about scene materials into MTX file.
When do publisher->Publish() to mts/mtx files, it doesn't. Is there any way to switch it on??

I am not sure that i understand what you want to achieve, but try following:

publisher->SaveMTXFile()
publisher->FlushSavedObjects() // maybe you don't need this
publisher->SaveMTSFile()